Question

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Answer 1

Answer:

51.2 minutes

Step-by-step explanation:

The Volume of  the conical vessel

=πr²h/3 where r =40/2=20cm

=π20²×24/3

=3200π cm3

the Volume of water flowing through the Pipe per minute

=Length of water passing through pipe × cross sectional Area of pipe

length of water =10m=1000cm

Area of pipe = πr² =π(0.25cm)²

=0.0625π cm²

=1000cm ×0.0625π cm²

=62.5π cm³/minute

Time taken to fill 3200π cm³ volume with speed 62.5π cm³/minute

= 3200π/62.5π

=51.2 minutes

Answer 2

Answer:

51.2 minutes

Step-by-step explanation:

Let the conical vessel be filled in 'x' minutes.

(i)

Diameter of cylindrical pipe = 5 mm.

Then, radius of cylindrical pipe = (5/2) = 2.5 mm = 0.25 cm.

Rate of water flow(h) = 10 m/min

                                  = 1000 cm/min

(ii)

Diameter of conical vessel = 40 cm.

Then, radius of conical vessel (R) = (40/2) = 20 cm.

Depth (H) = 24 cm.

Now,

Volume of water flowing in cylindrical pipe in 'x' mins = volume of conical vessel.

⇒ πr²h = (1/3)πR²H

⇒ 1 * (0.25)² * 1000x = (1/3) * (20)² * 24

⇒ 0.0625 * 1000x = (1/3) * 9600

⇒ 0.0625 * 1000x = 3200

⇒ 1000x = 51200

⇒ x = 51.2

Therefore, it will take 51.2 minutes to fill the vessel.

Hope it helps!